The son of one of America’s richest men pleaded with Peter Bacanovic to betray his social-circuit life of discretion and good taste to rat out Martha Stewart – but neither the handsome stockbroker nor his mom would hear a word of it, The Post has learned.

Bacanovic’s close pal, George Lindemann Jr, whose father, George, is worth an estimated $1.1 billion, offered his advice after being entangled in a federal insurance-fraud investigation, which resulted in him being sent to prison for 33 months, said Bacanovic’s mother, Helen Bacanovic.

“George told Peter, ‘You better cooperate or they’ll put you in jail,’ ” she told The Post only hours after watching her son lose his disastrous battle with the feds.

The Lindemanns, whose fortune is built on natural-gas distribution and cellular-phone empires, are one of the many well-heeled families the style-conscious Bacanovic counts as friends.

George Jr., who attended New York’s prestigious Lycée Francais with Bacanovic’s brother Paul, pleaded guilty in 1996 to lying to an insurance company about the 1990 electrocution of his equestrian horse, Charisma.

Bacanovic’s mother, a 72-year-old doctor, said federal investigators approached her son in 2002 in a bid to build up their case against Stewart after his Merrill Lynch assistant, Douglas Faneuil, began cooperating.

“Peter asked me, ‘How could I lie against this woman?’ ” she recounted.

“I said, ‘I won’t speak to you again if you say those things. One day you will answer to God and that’s the most important thing.’ “

Another friend said Bacanovic, whose career was built on connections to New York’s elite, couldn’t have “faced anyone” if he helped the feds nail Stewart – his top client.

Helen Bacanovic, who attended each day of her son’s grueling trial, described herself as “still feeling numb” as she tried to make sense of her son’s devastating descent from cultured financial adviser living in the Upper East Side digs featured in “Breakfast at Tiffany’s,” to a convicted criminal headed for prison.

“Peter’s father [Rade] is frozen – he cannot even speak a word,” she said.

“I can’t imagine he will go to prison – he is loved by so many people. He’s intelligent, a tremendous organizer, he’s very artistic and very giving.

“He was too decent for Wall Street. I am very proud of him.”

Barely containing her anger through a 45-minute interview, the feisty mother, who practiced as an anesthesiologist specializing in brain surgery, railed against her son’s judge, Miriam Goldman Cedarbaum, and his lawyers, Richard Strassberg and David Apfel.

She said she tried to convince the legal team to allow her son to testify.

“I personally wanted him to take the stand. Who will fight better for your life than yourself?” she said. “But the lawyer said no – under no circumstances.

“They were full of fears, always saying to Peter, ‘Don’t do this, don’t go out, don’t talk to Martha.’ “

She said Apfel’s brutal, seven-hour cross-examination of Faneuil backfired, making the rookie broker “look like an angel.”

“I asked [Apfel] to try a different approach, but he continued.”

Despite signs the trial wasn’t progressing well, she said her son “was always thinking he would be free.” Even when the judge indicated on Thursday that jurors could use two pieces of critical evidence from Stewart assistant Ann Armstrong to convict Bacanovic of perjury, he told his mother “not to worry, that the lawyers will find the right cases to convince the judge that was wrong,” she said.

“I said, “Look, [the judge] doesn’t want to see the other cases.”

When the shock verdict rolled in – with the 41-year-old being found guilty of obstructing justice, lying to federal agents, perjury and conspiracy – he was left in a daze and motioned to his lawyers to leave the courtroom quickly.